1. Field of the Invention
This invention relates to an apparatus and method for determining paperboard thermal conductivity. Such structures of this type, generally, determine the thermal conductivity of a planar material, such as paperboard or insulating foams. The apparatus is designed to characterize the heat flow from a heated brass cylinder, through a flat paperboard sample, and into another brass cylinder. The brass cylinders are fully insulated, except at the sample interface. During the test, which is in a transient state, the hot mass loses energy, raising the temperature of the cooler mass as the two masses approach an intermediate equilibrium temperature. Knowing that the brass masses are fully insulated, except for the heat transfer interface, and knowing the physical properties of the masses, the only unknown in the mathematical model describing the experiment is the thermal conductivity, k, of the paperboard sample, which enables its determination.
2. Description of the Related Art
A number of devices are available, or have been reported, for the determination of thermal conductivity of planar materials. A device which takes two to three hours for a single test named the Fox 300 Heat Flo Meter was developed by Laser Corp. The cost to measure a single sample on that device is over $800 per sample.
A method for determining the thermal conductivity and contact resistance of paper has been proposed, but this method requires a large size sample to be wrapped around a cylinder. Exemplary of such prior art is an article to R. J. Kerekes, entitled "A Simple Method for Determining the Thermal Conductivity and Contact Resistance of Paper," TAPPI Journal, Vol. 63, No. 9, September 1980, pp. 137-140. The size of samples under current consideration for the present invention are not adequate for this type of test.
A planar and smaller version of such a test has been reported by Asensio and Seyed-Yagoobi. See, for example, M. C. Asensio et al., entitled "Thermal Contact Conductance of a Moist Paper Handsheet/Metal Interface for Paper Drying Application," Journal of Heat Transfer, Technical Notes, Vol. 115, November 1993, pp. 1051-1053 and J. K. Seyed-Yagoobi et al., entitled "Thermal Contact Conductance of a Bone-Dry Paper Handsheet/Metal Interface," Journal of Heat Transfer, Vol. 114, May 1992, pp. 326-330. This method, although adequate, has more of a focus on thermal contact resistance of paper on a metal interface for study of paper machine drying. Samples for this test must be cut to precise dimensions. This is not conducive to the current needs of the present invention. The test of a single sample on this apparatus has been reported to take up to eight hours to complete.
Thermal conductivity of small paperboard samples has been determined using a differential scanning calorimetry (DSC) device. Exemplary of such prior art is discussed by S. M. Marcus et al., entitled "Thermal Conductivity of Polymers, Glasses, and Ceramics by Modulated DSC," TA Instruments, Document TA-086. The sample size for these tests is approximately 1/4 in. diameter. Even with the small sample size, a single test can take hours to perform and the small scale can raise questions when the nonuniformity of paperboard is of the same order of magnitude. Also, this is a "modulated" frequently-domain test where the thermal conductivity is backed out from repeated heating/cooling cycles. The size of the sample is simply too small to be representative of a paperboard packager length scales of interest.
There is an ASTM standard test for thermal conductivity and several experimental setups are described. See, for example, R. E. Mark, entitled Handbook of Physical and Mechanical Testing of Paper and Paperboard, Vol. 2, Chap. 23, "Thermal Properties," July 1984, pp. 241-279 and ASTM Standard Test Methods, C177-85 (1993) el, Summary of "Standard Test Method for SteadyState Heat Flux Measurements and Thermal Transmission Properties by Means of the Guarded-Hot-Plate Apparatus," 1997, ASTM, West Conshohucken, Pa. General features of the ASTM apparatus are shown in FIG. 2 on page 246, Nakagawa et al., in the Volume of Mark. This test falls into the category of a "steady state" device. It appears that the heat flux from one hot plate to another is the measured quantity and thermal conductivity is inferred from the experiment using Fourier's law.
Terasaki also uses a steady state method in which the sample is wrapped around a small diameter heated copper tube. See, for example, K. K. Terasaki et al., entitled "The Study of the Effective Thermal Conductivity of Papers for Temperature and Humidity, 2nd Report," Japan TAPPI, Vol. 26, No. 10, pp. 511-515, 1972. A schematic of the device is shown in FIG. 3 on page 248 of the R. E. Mark reference. The low-temperature-differential system consists of transferring heat from the heated tube, through the wrapped sample, to a controlled air environment. This apparatus is not exactly conducive to testing single plies of "hard to wrap" paperboard, polystyrene, and composite samples.
Terada discloses a method by which paperboard samples are studied in a controlled, low pressure, nitrogen environment condition in a steady-state experiment. See, for example, T. N. Terada et al., entitled "Effective Thermal Conductivity of Insulating Paper," Japan TAPPI, Vol. 23, No. 5, pp. 191-197, 1969. A schematic of the device is shown in FIG. 4 on page 248 of the R. E. Mark reference.
A "transient-state" experiment has been devised by Kirk and Tatlicibasi in which a flash power pack and flash tube are used as an energy source. See, for example, L. A. Kirk et al., entitled "Measurement of Thermal Conductivity of Paper by a Heated Pulse Method," TAPPI, Vol. 55, No. 12, pp. 1697-1700, 1972. A schematic of the device is shown in FIG. 5 on page 249 of the R. E. Mark reference. The thermal conductivity of the sample is backed out from the experiment by way of the sample's thermal diffusivity, .alpha.=k/(.rho.C). The drawback of this approach is that the specific heat C and density .rho. for the sample must be known. This is not the case for the present invention, in which the density and specific heat of the known brass masses are needed, and held as constants in all tests of paperboard samples.
It is apparent from the above that there exists a need in the art for an apparatus which can easily, precisely and repeatably measure the thermal conductivity of a paperboard sample. It is the purpose of this invention to fulfill this and other needs in the art in a manner more apparent to the skilled artisan once given the following disclosure.